1. Field of the Invention
The present invention relates to a wireless system, and more particularly to a carrier frequency offset estimation method and system.
2. Description of the Related Art
Conventionally, a carrier frequency offset value is usually calculated by the delay correlation value in time axis, and a basic requirement of the carrier frequency offset estimation method is that the preamble signal comprises at least two identical signals, wherein the two identical signals may be composed of two or more OFDM (Orthogonal Frequency Division Multiplexing) symbols, or two or more identical signals in one OFDM symbol. According to the identical feature, a delay correlation value generated by the two identical signals can be used to estimate the carrier frequency offset value. The basic idea can be interpreted by the following equations.
                    z        =                              ∑                          n              =              0                                      N              -              1                                ⁢                                    r              n                        ⁢                          r                              n                +                D                            *                                                              =                              ∑                          n              =              0                                      N              -              1                                ⁢                                    s              n                        ⁢                                                            ⅇ                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      Δ                                        ⁢                                          nT                      s                                                                      ⁡                                  (                                                            s                                              n                        +                        D                                                              ⁢                                          ⅇ                                              j2π                        ⁢                                                                                                  ⁢                                                                              f                            Δ                                                    ⁡                                                      (                                                          n                              +                              D                                                        )                                                                          ⁢                                                  T                          s                                                                                                      )                                            *                                                                        =                                    ⅇ                                                -                  j                                ⁢                                                                  ⁢                2                ⁢                π                ⁢                                                                  ⁢                                  f                  Δ                                ⁢                                  DT                  s                                                      ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                                                      s                    n                                                                    2                                                    ,                                  ⁢        wherein            
z is a delay correlation function to show the sum of the product of data value at two corresponding position in the received signal;
rn is the data value at nth point of the received signal;
rn+D is the data value at (n+D)th point of the received signal;
sn is the data value at nth point of the transmitted signal;
sn+D is the data value at (n+D)th point of the transmitted signal;
fΔ is the carrier frequency offset;
Ts is sampling period;
D is the delay length, wherein the data value at nth point of the received signal is the same as the data value at (n+D)th point of the received signal when no noise and frequency offset occur; and
* means to calculate the corresponding complex conjugate.
According to the delay correlation function, it can be found that the carrier frequency offset is determined based on the phase of the function, and the carrier frequency offset can be acquired after the phase of the function is normalized. The carrier frequency offset can be shown as the following:
            f      ^        Δ    =            -              1                  2          ⁢          π          ⁢                                          ⁢                      DT            s                                ⁢    ∠    ⁢                  ⁢    z  
In the standard of IEEE 802.16e, the preamble symbol has three repeat segments in time domain and the delay correlation technique can be applied to the carrier frequency offset estimation. However, after sampling, the three repeat signals may not have the repeat feature. In other words, a phase offset is generated and this causes an undesired phase term, wherein the undesired phase term is different according to the preamble signals in different sectors. Please refer to FIGS. 1a and 1b. FIG. 1a and FIG. 1b are schematic diagrams of data values determined by sampling the three repeat signals with different sampling rates in the discrete time domain. In FIG. 1a, we find that the data values at the corresponding positions in the three repeat signals are the same and this is because the three repeat signals are sampled by 9 points. However, in the FIG. 1b, the data values at the corresponding positions in the three repeat signals are different and this is because the three repeat signals are sampled by 10 points. In the IEEE 802.16e standard, the preamble signal has three-repeat feature. But in the receiver design, if the sampling rate is not the threefold system bandwidth or multiple of 3, say, twofold or fourfold. In such cases, it will cause the same phenomenon shown in FIG. 1b and the undesired phase term is generated during the delay correlation computing procedure. The described phenomenon can also be observed by mathematical operations. Please refer to the following equations.
                                                        z              =                                                ∑                                      n                    =                    0                                                        N                    -                    1                                                  ⁢                                                      r                    n                                    ⁢                                      r                                          n                      +                      D                                        *                                                                                                                          =                                                ∑                                      n                    =                    0                                                        N                    -                    1                                                  ⁢                                                      a                    n                                    ⁢                                                                                    ⅇ                                                  j                          ⁢                                                                                                          ⁢                          2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            Δ                                                    ⁢                                                      nT                            s                                                                                              ⁡                                              (                                                                              a                                                          n                              +                              D                                                                                ⁢                                                      ⅇ                                                          j2π                              ⁢                                                                                                                          ⁢                                                                                                f                                  Δ                                                                ⁡                                                                  (                                                                      n                                    +                                    D                                                                    )                                                                                            ⁢                                                              T                                s                                                                                                                                    )                                                              *                                                                                                                          =                                                ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      Δ                                        ⁢                                          DT                      s                                                                      ⁢                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                                                                          a                        n                                                                                    2                                                                                                          (                  Eq          .                                          ⁢          1                )                                                                    z              =                                                ∑                                      n                    =                    0                                                        N                    -                    1                                                  ⁢                                                      r                    n                                    ⁢                                      r                                          n                      +                      D                                        *                                                                                                                          =                                                ∑                                      n                    =                    0                                                        N                    -                    1                                                  ⁢                                                      a                    n                                    ⁢                                                                                    ⅇ                                                  j                          ⁢                                                                                                          ⁢                          2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            Δ                                                    ⁢                                                      nT                            s                                                                                              ⁡                                              (                                                                              a                                                          n                              +                              D                                                                                ⁢                                                      ⅇ                                                          j2π                              ⁢                                                                                                                          ⁢                                                                                                f                                  Δ                                                                ⁡                                                                  (                                                                      n                                    +                                    D                                                                    )                                                                                            ⁢                                                              T                                s                                                                                                                                    )                                                              *                                                                                                                          =                                                ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      Δ                                        ⁢                                          DT                      s                                                                      ⁢                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                                                                          a                        n                                                                                    ⁢                                          ⅇ                                              j                        ⁢                                                                                                  ⁢                                                  θ                          n                                                                                      ⁢                                                                                        a                                                  n                          +                          D                                                                                                            ⁢                                          ⅇ                                              -                                                  jθ                                                      n                            +                            D                                                                                                                                                                                                                      =                                                ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      Δ                                        ⁢                                          DT                      s                                                                      ⁢                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                                                                                                      a                          n                                                                                            ·                                                                                                a                                                      n                            +                            D                                                                                                                                        ⁢                                          ⅇ                                              -                                                  j                          ⁡                                                      (                                                                                          θ                                                                  n                                  +                                  D                                                                                            -                                                              θ                                n                                                                                      )                                                                                                                                                                                                                      =                                                ⅇ                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      Δ                                        ⁢                                          DT                      s                                                                      ⁢                                                      ∑                                          n                      =                      0                                                              N                      -                      1                                                        ⁢                                                                          ⁢                                                                                                          A                        n                                                                                    ⁢                                          ⅇ                                              j                        ⁢                                                                                                  ⁢                        Θ                                                                                                                                                    (                  Eq          .                                          ⁢          2                )            
The equation Eq. 1 shows the delay correlation of the signal with repeat feature. The equation Eq. 2 shows the delay correlation of the signal with non-perfect repeat feature. According to the equation Eq. 2, an undesired phase term Θn is generated, and after eliminating the undesired phase term, Θn, the accurate carrier frequency offset is then calculated.